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arXiv · 1104.2206

The Hausdorff dimension of graphs of prevalent continuous functions

Jonathan M. Fraser·James T. Hyde
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Abstract

We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2. We also indicate how our results can be extended to the space of continuous functions on $[0,1]^d$ for $d \in \mathbb{N}$ and use this to obtain results on the `horizon problem' for fractal surfaces. We begin with a survey of previous results on the dimension of a generic continuous function.

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Jonathan M. Fraser, James T. Hyde. 2011-04-12. The Hausdorff dimension of graphs of prevalent continuous functions. https://arxiv.org/abs/1104.2206

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